#include "../src/dyadicp.cc"

#include <cassert>
#include <iostream>

namespace
{
  std::ostream&
  operator<< (std::ostream& o,
              std::pair<bool, float>& p)
    {
      return o << "{ " << (p.first ? "true" : "false") 
               << ", " << p.second
               << " }";
    }
}

namespace
{
  bool
  fuzzy_eq (float a,
            float b)
    {
      return fabs (a - b) <= 1e-5 * (1.0 + fabs (a) + fabs (b));
    }

  struct PFuncTestData
    {
      float s;
      float adotb;
      float anormplusnorm;
      float wdotx;
      float xnorm;
      float onedotone;
      float p;
    };

  std::ostream&
  operator<< (std::ostream& o,
              const PFuncTestData& t)
    {
      return o << "{ " 
               << t.s << ","
               << t.adotb << ","
               << t.anormplusnorm << ","
               << t.wdotx << ","
               << t.xnorm << ","
               << t.onedotone << ","
               << t.p 
               << "}";
    }

  void
  test_pfunc ()
    {
      unsigned int precision_fail = 0;
      PFuncTestData test_data[] = {
{4.411479019238321, 0, 0, 0.12100892882633041, 0.10716087095435042, 0.5042403653775976, -0.8559693704496893},{3.497087407284117, 0, 0, -0.39483243578481253, 0.7270841149781363, 0.7955516643683704, -3.7330608026795407},{4.619261689794473, -0.3905816394596368, 0.7123563495038744, 0.274333647570285, 0.024986830660902147, 0.34056667272547353, -3840.707287698399},{-4.161610712629299, 0.12851666895248215, 0.606274481710778, 0.21955774389914318, 0, 0.2153173785215455, 888.8672016326307},{-3.7303068294569215, 0, 0, -0.38985018569364194, 0.3998852020761716, 0.31459814993798757, 0.7872461646718745},{-0.6204096690327571, 0.40476465501874825, 0.7709632326539034, 0.040264502367702515, 0.41297220243582217, 0.19969782964222896, 1.4660784432103473},{-1.7086672630124795, -0.19197318809614983, 0.1814296940755704, -0.019859914256914246, 0, 0.2648227072215403, -1.832902923421394},{-2.7451410113827546, 0.11434063588362742, 0.04144381706883847, -0.34532710708481773, 0.8256006967855529, 0.8400747429771948, 17.445733555360004},{-1.1235833631117136, 0.19539296530576777, 0.7871610022571571, -0.20018975939050782, 0.9746694612530065, 0.10011241096726325, 3.57045351472415},{1.4553618755425446, -0.04917732745441461, 0.8180271323952383, 0.11997232522417745, 0.293080971638222, 0.35514961800263717, -4.860425862727248},{-4.324049272235025, -0.37241365632702683, 0.756393189719757, -0.29952327491254505, 0, 0.3604019821102602, 15.819358119882608},{3.5435271230211587, 0, 0, -0.439408258499232, 0.8796832510491094, 0.9604793305335048, -4.517069048792687},{-2.658529365051451, 0.12236360104766841, 0.5936239936854922, -0.15949299469067268, 0.9410660918566329, 0.9853573873066901, 44.067133189886405},{3.734710190801355, 0.25285027781809466, 0.039393797177139714, 0.28488066221923525, 0.6314766430891909, 0.424478680108975, 201.92981200897},{2.7712393078707507, -0.10661420357305179, 0.430016889816904, -0.13611306139179302, 0, 0.40340760807470216, -41.59605261762421},{1.632936162431109, 0.19783592178602594, 0.42474177005068126, -0.4370993972346251, 0.722227524386478, 0.07754321545868476, -1.8765960838731746},{3.487565053063425, -0.4354509775231366, 0.5895609859766447, -0.20733744676055044, 0.21727986221715154, 0.8681838731304746, -392.3963356164591},{-0.5984406856992358, 0, 0, 0.004296934522267648, 0.5427152516921107, 0.10088932644756546, 0.22819049543676226},{3.794216354489998, -0.07229377303944262, 0.8753117200044428, -0.4620112763178094, 0.1571941110625218, 0.9604455082235058, -505.64896402604757},{-1.915623942438207, 0.04575790418873593, 0.6567959508740134, 0.16778295498405627, 0.09115774353902774, 0.7995990818535816, 8.167788498677824},{1.5100181210895125, 0, 0, -0.204697852668686, 0.10828656041684065, 0.19441282088374853, -0.5626253420523183},{-2.711350750321591, 0, 0, -0.343575902798442, 0, 0.19597858897805215, -0.5395544917764942},{2.6323320814913975, 0.05157555803975644, 0.5114224556902761, 0.02819563399399594, 0.672075464610112, 0.7285965521404143, -22.20674825315969},{-4.789263474988392, 0.08405635725701399, 0.0131220949499495, -0.06670559519089975, 0.9127870920843201, 0.2388815839253517, 658.8273251444714},{1.8392216711647924, 0.24106935250827344, 0.3086596881156111, -0.4175425132762063, 0, 0.8864788977457416, 0.41775277661183563},{3.490181450620203, -0.40783966775997527, 0.6290188258610454, -0.14171673624825432, 0, 0.6296867116113314, -389.1455098115648},{-3.4413097204925247, 0.1631588531247643, 0.012834082486631886, -0.3036076931977688, 0.2430819358664274, 0.9575107228768794, 82.25877519183403},{0.5915976874994822, -0.02662024078587416, 0.9809393628404619, 0.3750532361530857, 0.946908415538788, 0.9885743384073441, -1.9467666992180717},{-4.021097295232323, 0.23748353669431999, 0.2114792554280949, 0.13029107465559842, 0, 0.0006043630442670472, 533.7438468931804},{2.65078562074112, 0.3271094731877774, 0.17268899550488162, 0.30421205624203584, 0.5219966262076845, 0.8467013333651564, 22.229806900266333},{4.628368574577363, -0.3607193977487477, 0.9021505817083468, 0.4716480972120707, 0, 0.9830737588047265, -4252.245304621609},{4.180381714421806, 0, 0, -0.14721731585087194, 0.9970905814173211, 0.352178321104861, -4.6676148711349095},{-2.6798798065679073, -0.24522460287773157, 0.4919611714947164, 0.04796626486282518, 0.7100153931355248, 0.7012649314976688, 1.328691296447809},{2.4717853567778834, 0, 0, 0.2296168342855981, 0.7312500937588401, 0.7465430754808715, -2.3244195150908284},{3.132119223166595, 0.12104450346614282, 0.7948948998272429, -0.10623960866825655, 0, 0.04158207022688247, -72.76408753146121},{0.8410932155612916, -0.21561576396617138, 0.6382835613329285, -0.006384194635942642, 0, 0.7923508738663886, -2.226884793161682},{-3.7308460725718398, -0.3605652330286996, 0.32269168914945984, -0.43726596041920945, 0.3956652989839759, 0.31619096409991904, -172.60727861513556},{0.8245337666731634, -0.17480743658357284, 0.8827286445038623, 0.4224305727681755, 0.7663320357679779, 0.8808485025412931, -2.6673663745268597},{-3.1777728578815125, 0.0016486942265014903, 0.11420035034328888, -0.11276730282276426, 0, 0.5948818233108472, 16.20247184418707},{-3.187866069515717, 0.21994472687826272, 0.7620963268068083, 0.032147783730056556, 0, 0.21595681963013758, 176.33227630138822},{-2.9690528260286397, -0.05148490342073453, 0.20174413797184054, -0.206473753138038, 0.43676268162915804, 0.41267774432066895, 10.041617863806723},{-2.454600325826908, -0.3391665279075662, 0.3350598759523342, -0.4745549528565668, 0.9464111816260649, 0.43056322383258605, -10.214968585808},{2.6519778857763656, 0.08150925136460796, 0.48817553318925794, 0.3984154401025295, 0.9796496945131842, 0.6824586204723919, -19.2310218826265},{2.7655497711604813, -0.1407135052103502, 0.20195861274171448, -0.11106762638957013, 0.33979229548689016, 0.9762546292897609, -32.531321090308175},{-4.147476719304191, 0.03597085637828068, 0.4176385104937571, 0.4508095821463277, 0, 0.5202463583137417, 489.95344677961634},{-1.263566421341205, 0.15300762677080204, 0.6791911173084331, 0.12183091821121217, 0.39399366335269526, 0.9393722977388202, 2.7559388886806975},{1.174386862366471, -0.014080459387763034, 0.07352975385316352, 0.05043992412839038, 0.27764639074975694, 0.5741852948386295, -1.114971090447562},{-3.07605937319824, 0, 0, 0.12337571269230174, 0.05355291623665999, 0.10312935437856001, 0.1849783082656199},{1.7990955837078049, -0.13438014914297008, 0.05663508910719102, -0.0187015638326522, 0.28591589501808523, 0.5419261384285275, -4.0483130984848685},{1.6847720878143813, -0.46550572515709376, 0.7076169686591495, 0.49148621430013706, 0.3908308180316812, 0.4173009194615076, -12.492993607385383},{-3.015632446484948, 0.49223470693814186, 0.48359274433876237, 0.29392520676920597, 0.14488383911484518, 0.6907958523906459, 152.80733413300092},{-0.3502571925593534, 0, 0, -0.2905025837767019, 0.1790583857259794, 0.6675712777947707, -0.8953573740828812},{0.10581176944541304, -0.44692071184476945, 0.20236775764448475, 0.1760850634946335, 0.1197503589128601, 0.2587841440331259, -0.573908835959189},{4.21313603561355, 0.31546551851570503, 0.331989412053645, -0.03514106273608003, 0.7764297644465098, 0.774063084873274, 337.12030480560753},{-1.8854451629755486, 0, 0, 0.06456566864997593, 0.13239709797646573, 0.8969943908552054, -0.5828012542335024},{1.218159210319244, -0.40678194040125226, 0.7807389413664405, -0.27909067263942816, 0.5020655621190644, 0.962125183327446, -6.409600403067806},{0.8075195855770945, -0.029947684370804084, 0.633167372920388, -0.002733753936474015, 0, 0.7232031611902519, -1.5686279906301233},{-0.0713328959124554, -0.10567688432831429, 0.15585307347532185, -0.3413625074597241, 0, 0.26164310168507054, -0.6986045648375927},{2.386536914003643, -0.3451922916810404, 0.3920074330979561, -0.4592662256755013, 0.23658812928129996, 0.07860859099705275, -33.11007607751957},{1.5583617072359057, -0.10076244145513719, 0.793683275203535, 0.08134234493352677, 0.8515139766123909, 0.8581391837432749, -7.713238997540639},{-1.4135273379636355, 0, 0, 0.19950169120299888, 0.9981776537713477, 0.4378585895179284, 1.172594503435271},{-2.4047603762901657, 0, 0, -0.10287518480657032, 0.022935833089683437, 0.31851622419637693, -0.3662362263916717},{-1.3290033763390712, 0.20535950749378784, 0.803597972048521, 0.23717387926285016, 0, 0.8790346955195752, 3.6826696653375204},{-3.430615804499345, 0.057595558923349444, 0.4699734926965357, -0.3204669956834236, 0, 0.741674414798648, 138.57881016072992},{3.9923680340773435, -0.04498602982102895, 0.029702268846621565, -0.1554504003947817, 0.8763009703180509, 0.026033375408841403, -91.51504860798805},{0.0920130795195806, 0.1450573966465326, 0.6288230495460445, -0.21114050385400873, 0.9936156221982562, 0.40982480062641596, -0.6230574475057757},{3.3667720264819065, -0.34685413764954254, 0.09999036121464142, -0.26970820369016035, 0, 0.4886173815111916, -167.45891256342452},{2.786796334617385, -0.23076901822019408, 0.016453928145419284, -0.3559322180940267, 0.9023786631436876, 0.1180344064971319, -34.46235230566402},{-1.0682264480827048, -0.22624331900704714, 0.9552098570048092, 0.32917491035114066, 0.3995617329934734, 0.4193501097247247, 1.3595283028834992},{0.6288453034528274, -0.09013060263131145, 0.28525564187899066, -0.3109416865851149, 0.8849680934758098, 0.7004409319036935, -1.9697672656132728},{-3.937115399859286, -0.08360653636989435, 0.2226455167415305, 0.05637314999772014, 0.20390979687038377, 0.43833874350058827, 36.849123517115984},{3.1073244167865424, -0.2761772950023327, 0.6834027531858676, 0.10916383314944766, 0.4111707086851808, 0.18981372342472294, -155.83418552363608},{3.4828617833989792, -0.2490619520901673, 0.01290110821324496, -0.49924458999016214, 0.9633180848640881, 0.3003144781061444, -139.5357011961333},{3.570296248500168, -0.35107986113018447, 0.5511561465847646, 0.24394132810842428, 0.653119827979633, 0.305602584607836, -397.8698259254111},{3.4238738630097876, -0.07248195211847192, 0.22914078320822023, 0.1964387514583884, 0.43121667761579796, 0.5066250280336655, -89.8655618038888},{0.8293049927590002, 0.015772554693174068, 0.9180829249027397, 0.005869618023827572, 0, 0.20555513991768318, -1.3185077557231542},{2.6258278956179515, 0, 0, -0.03838618819074108, 0.10946296158216216, 0.15601122720142294, -0.4818283134515615},{-2.329244247188166, 0.22268001256271397, 0.4514407953893717, -0.04042752425696544, 0.8358588976653855, 0.9529474477093691, 24.601390531670955},{-2.470716016105145, -0.05980314473346693, 0.6023738373706474, -0.052922170314458505, 0.6333159839776736, 0.24152268976785832, 18.162319175855767},{3.707331944158785, 0.18819908974984279, 0.8649674608025231, 0.2799088779585994, 0, 0.6238976507571764, -203.1185066490063},{-0.0580534244746711, 0.3153210167428868, 0.7329450868155594, -0.3356748249858581, 0.6583357598871474, 0.2113777273047728, -0.14873947367433576},{-0.9459263850233801, -0.0808452484833534, 0.6101144871715249, 0.2642998976192312, 0, 0.5227772078513729, 0.4558742437195531},{4.0135818310410984, -0.2587822413064763, 0.287054450574799, 0.24286832989277363, 0, 0.11897067913559713, -616.0214211981979},{1.4589329271786067, 0, 0, 0.4546455041214552, 0, 0.7432677768166824, -0.2886222726952272},{0.8215017133305125, 0.10938935434520991, 0.5471206698406113, 0.4789678791974512, 0.8100587938130628, 0.4561906713460782, -1.030094038844931},{4.087006107089529, -0.061245252791680305, 0.10804430788849013, 0.21332234145330464, 0, 0.5943516623177075, -204.83941559489614},{-3.7728063227930138, 0.34764230517536054, 0.6356522579643138, 0.13970615819625232, 0.13516183488998543, 0.8964383813795699, 629.42668983472},{0.5301166355693421, -0.29029115503170577, 0.9312964311115665, 0.4174705021821187, 0.7429528697438714, 0.46127983083604046, -1.4985066070803286},{3.3425225903491853, -0.40901840814186885, 0.4281533647597871, 0.24795748938273587, 0.06563959859635923, 0.15360582706502837, -249.47126457238718},{4.429202308756606, 0.007801268862373867, 0.7871253672768511, 0.013899668868776138, 0.8077583959856751, 0.6174612874892063, -1360.7600839606637},{-2.452532675712591, -0.021005775419424333, 0.3774118352131071, 0.19999078530708758, 0.5117938626848695, 0.23871095447104712, 12.533083312055753},{1.7754160364995097, 0.35827629365599367, 0.4130607978050427, -0.009246534911688753, 0.6119020050535917, 0.3371476380232829, 1.2189181308200547},{1.6898177417793114, 0.4950314507558854, 0.20315780528702673, 0.3232479691545068, 0.8612233781922559, 0.2057866816653005, 4.448207552518053},{1.06476645763515, 0.32733415662643983, 0.5170377037492462, 0.005795896358212871, 0.09468278307864555, 0.2670849418871658, -0.03787663484961101},{-0.8285882057130539, -0.4802000225436787, 0.2627627433793736, 0.2763314767988545, 0.805239174375103, 0.43918383877557166, -0.4686343222751559},{-3.6374259980282817, 0.021935807082176684, 0.06932176552846904, 0.11593586962106484, 0, 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0.6108111631632153, 0.06335186334134013, 0.559756760968386, 0.5152900764664741, -1.1941991873451463},{-1.2881189488476537, 0, 0, -0.05225130895550828, 0.9565334457768053, 0.9609172535904442, 0.21896029416569007},{2.735815941494071, 0.41400153375836557, 0.740480236038311, -0.06692782933539843, 0.6138325206191872, 0.05768930033091072, 3.401981657754262},{-4.421480062035683, 0, 0, -0.005662563010429444, 0.49809523282804563, 0.9790473605230965, 1.2176082174106992},{-3.73092872287189, 0.11922150997486569, 0.9129634717781204, 0.031298669478604824, 0, 0.5703814158881606, 500.4313698911225},{-1.0320791221340149, 0.17253327906117166, 0.35689722803580487, -0.36269075477644097, 0.7829595671674112, 0.07961994489264827, 1.7480241825688243},{2.2510757337097953, 0.12787426996480022, 0.9775061023511343, 0.08528250790307768, 0.2270123405429339, 0.6062351473799812, -17.306176353893754},{-3.9989478716987708, 0.4603138538779573, 0.6649112666469225, -0.4250635220986236, 0.9297315308941173, 0.5045550620132159, 1181.910829602782},{0.3293944310751873, 0.20124576199724853, 0.21063657453700171, -0.13275418321034316, 0.7499798759401075, 0.2876258718970086, -0.49541167535916997},{-4.751276974308721, 0, 0, 0.20234336399393094, 0.797859962026194, 0.09610821661394967, 3.8970888136778674},{1.9775474919607106, -0.36990264000249984, 0.6285483835020402, -0.4788282612874267, 0, 0.5166166766993574, -18.853216097884726},{-2.6491622480556485, -0.44492744305816856, 0.8503780063922319, -0.35062914009029944, 0, 0.861744988012692, -3.1884074626108023},{-0.39768403314800305, -0.4126948684795298, 0.1302031268930866, -0.34059837598123893, 0.6623716346590056, 0.06329340740481139, -0.6333235246560083},{4.646168854629345, 0, 0, -0.45787833130776184, 0, 0.5255049919928807, -0.9833833233006426},{4.615098919665456, -0.4445943182333988, 0.29680250592061824, -0.1238658679168198, 0.476405992712218, 0.5143891440704883, -3027.2801994988013},{-4.838256039729816, -0.28915115900261973, 0.1650618635604395, -0.14501247994827277, 0.3538027613680127, 0.2916941126469158, -1645.3648475716252},{-1.1081412409492186, -0.15284163429514508, 0.12012329357423182, -0.2504275560453223, 0.19259220874409744, 0.7240674519617969, -1.1982234301338155},{-2.6891768322244824, -0.3187255547701789, 0.6761402753407635, -0.1520666801213833, 0.7546763240653338, 0.8335441758081285, 3.13798125333373},{2.385019280383154, 0.17227163171459037, 0.21581342132679787, -0.021443344243598783, 0.38469916667030274, 0.1868625431094854, 2.6704448344990346},{4.955132907652246, -0.3888416573426321, 0.7673717409362505, 0.43729009915480777, 0.8029210820211271, 0.21322264719301082, -7781.571607200421},{0.7183876524357535, 0.19320377043112458, 0.11828868433410528, 0.3652893273143941, 0.8171624411782415, 0.03174515150626564, 0.058496657833310206},{-4.213394868600738, -0.3621883339954365, 0.5215999781200701, 0.053188495749864395, 0.6939613464696235, 0.366325952640379, -228.95075481789655},{1.9844805570439894, 0.06833661498497279, 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158.64000851008717},{4.6475578974873235, 0, 0, -0.11291187716008694, 0.8168100489590828, 0.4668300207901481, -4.375913891737028},{2.0432016011693976, -0.0022319191311515607, 0.3074713529124678, 0.016800344336469264, 0.7317591495390313, 0.32118588718631613, -6.440261586955769},{0.75438808785661, -0.047460004197104166, 0.7166779286273797, 0.029462770361522228, 0.7288333705953741, 0.8228522663901869, -2.226180510689364},{2.640775808466418, 0, 0, -0.06423585644972618, 0, 0.9689341227601257, -1.0331699792098519},{-2.570526282293808, 0.04007107969529122, 0.8363314518397089, -0.047866221576343626, 0.5111882222315879, 0.13094789123734027, 40.28941842059688},{4.357494134459269, -0.33241542228100573, 0.6915009990182399, 0.10148512087581807, 0.20691604285055276, 0.7786328544856311, -2067.8022116136967},{-0.5716153799608903, 0, 0, -0.15713128906464263, 0, 0.3739345881752317, -0.5310658772398743},{-2.473764416542672, -0.0398013904703004, 0.3024685572324564, 0.4218008097515753, 0.7414353361141449, 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-0.8506888158075719},{-3.568604716075445, 0, 0, -0.12042568723235786, 0.697585643151971, 0.7601970140420837, 1.6087847147442045},{1.5976868726315607, 0.17849961647443624, 0.38308415885339986, 0.4129505496071467, 0, 0.046982000948596156, 0.2143014790358898},{2.7735363252988208, 0.051147707898120065, 0.3215550929133725, 0.472923570428015, 0.5282997311995397, 0.28004031489261766, -15.331201365460544},{-1.1483979719291582, -0.08265792225084884, 0.25883027966009675, 0.4004660021249755, 0.6875745596551132, 0.14026898808289182, 1.2715776020375875},{-4.721941276080429, 0.2260652477538665, 0.2889337010234823, -0.2726815615242549, 0.7395525477800913, 0.18033643752714895, 2343.071776134729},{4.621989152502092, 0, 0, -0.29258713290086613, 0, 0.9273725522065162, -1.2199596851073822},{-4.512610187564147, 0.16642068915080088, 0.8863877829076657, -0.4730934499184593, 0.3611644215884721, 0.8866375619986488, 2533.2325280288446},{-1.6664145080348498, 0.035790577168631654, 0.9254362220073012, 0.15931912352290378, 0.5938060014164238, 0.4789826859957548, 7.645725925096949}
};

      for (unsigned int n = 0;
           n < sizeof (test_data) / sizeof (test_data[0]);
           ++n)
        {
          std::pair<bool, float> p = 
            flassol::dyadic::p (test_data[n].s,
                                test_data[n].adotb,
                                test_data[n].anormplusnorm,
                                test_data[n].wdotx,
                                test_data[n].xnorm,
                                test_data[n].onedotone);

          assert (fuzzy_eq (test_data[n].p, p.second)
                  || p.first
                  || (std::cerr << "test_data = " << test_data[n]
                                << " p = " << p 
                                << std::endl,
                      0));

          if (p.first) { ++precision_fail; }
        }

      std::cerr << __FUNCTION__ 
                << " info: " << precision_fail 
                << " out of " << sizeof (test_data) / sizeof (test_data[0])
                << " catastrophic cancellations detected"
                << std::endl;
    }

  bool
  test_pinvfunc_once ()
    {
      float a = (drand48 () < 0.25) ? 0 : 2.0 * drand48 () - 1.0;
      float b = (drand48 () < 0.25) ? 0 : 2.0 * drand48 () - 1.0;
      float x = (drand48 () < 0.25) ? 0 : 2.0 * drand48 () - 1.0;

      while (a == 0 && b == 0 && x == 0)
        {
          a = (drand48 () < 0.25) ? 0 : 2.0 * drand48 () - 1.0;
          b = (drand48 () < 0.25) ? 0 : 2.0 * drand48 () - 1.0;
          x = (drand48 () < 0.25) ? 0 : 2.0 * drand48 () - 1.0;
        }

      float w = drand48 () - 0.5;
      float adotb = a * b;
      float anormplusnorm = a * a + b * b;
      float wdotx = w * x;
      float xnorm = x * x;
      float onedotone = 2.0 * drand48 () - 1.0;
      float p = 2.0 * drand48 () - 1.0;

      std::pair<bool, float> s = 
        flassol::dyadic::pinv (p, adotb, anormplusnorm, wdotx, xnorm, onedotone);

      std::pair<bool, float> ps = 
        flassol::dyadic::p (s.second, adotb, anormplusnorm, wdotx, xnorm, onedotone);

      assert (fuzzy_eq (ps.second, p) || s.first || 
              (std::cerr << " p = " << p
                         << " s = " << s 
                         << " ps = " << ps
                         << " a = " << a
                         << " b = " << b
                         << " x = " << x
                         << " onedotone = " << onedotone
                         << " fabs (" << ps.second << " - " 
                                      << p << ") = " 
                                      << fabs (ps.second - p)
                         << " 1.0 + fabs (" << ps.second << ") + "
                                   "fabs (" << p << ") = "
                                            << 1.0 + fabs (ps.second) 
                                                   + fabs (p)
                         << std::endl,
               0));

      return s.first;
    }

  void
  test_pinvfunc ()
    {
      unsigned int precision_fail = 0;
      unsigned int count = 1000000;

      for (unsigned int n = 0; n < count; ++n)
        {
          if (test_pinvfunc_once ())
            {
              ++precision_fail;
            }
        }

      std::cerr << __FUNCTION__ 
                << " info: " << precision_fail 
                << " out of " << count << " failures to invert detected"
                << std::endl;
    }
}

int 
main ()
{
  srand48 (69);

  test_pfunc ();
  test_pinvfunc ();

  return 0;
}
